Initially, when Sona and Tina left for a shopping expedition, Sona had three…
2025
Initially, when Sona and Tina left for a shopping expedition, Sona had three times the money than Tina had. They bought things amounting to Rs. 480 altogether, out of which Tina's share was 65%. At the end of shopping, Sona was left with 4 times the amount that Tina had. What was the amount with Tina at the beginning?
- A.
936
- B.
1080
- C.
768
- D.
1248
Show answer & explanation
Correct answer: B
Concept: In word problems that give a ratio between two people's opening amounts and a further relationship after a shared expense, assign a variable to one person's opening amount, express the other via the given ratio, form a linear equation from the post-expense relationship, and solve.
Let Tina's opening amount be T. Since Sona had three times Tina's amount, Sona's opening amount is 3T.
Total amount spent by both = Rs. 480. Tina's share = 65% of 480 = Rs. 312, so Sona's share = 480 - 312 = Rs. 168.
Amount remaining after shopping: Tina = T - 312; Sona = 3T - 168.
Given that Sona's remaining amount is 4 times Tina's remaining amount: 3T - 168 = 4(T - 312).
Expand: 3T - 168 = 4T - 1248.
Solve: 4T - 3T = 1248 - 168, so T = 1080.
Cross-check: With T = 1080, Sona's opening amount = 3 × 1080 = 3240. After shopping, Tina has 1080 - 312 = 768 and Sona has 3240 - 168 = 3072. Since 3072 = 4 × 768, the relationship holds, confirming Tina had Rs. 1080 at the beginning.